Question

What is the vertex form of `y= 9x^2 + 2x + 2/7`?

Answer 1

See below:

Explanation:

The vertex form of a quadratic equation is

`y=a(x-h)^2+k` with `(h,k)` as the vertex.

To find the vertex form of a quadratic equation, complete the square:

`y=9(x^2+2/9x+(1/9)^2-(1/9)^2)+2/7`

`y=9(x+1/9)^2-9/81+2/7`

`y=9(x+1/9)^2+11/63`

The vertex is `(-1/9,11/63)`

You can also find the vertex with formulas:

`h=-b/(2a)`

`k=c-b^2/(4a)`

`------------`

`h=-2/(2*9)=-1/9`

`k=2/7-(-2)^2/(4*9)=2/7-4/36=11/63`

so the vertex is at

`(-1/9,11/63)`

You can also find vertex form this way:

`y=a(x+1/9)+11/63`

Plug in `a` from the original equation:

`y=9(x+1/9)+11/63`

Apologies for the length :)